ACCEPTED MANUSCRIPT of a Catmull a surface by its limi mesh Zhangjin Huang Jiansong Deng,Guoping Wang CCSS. nd on CCSS a eaa.Pt epth csti 1ga1the.T:+861062765819 29Mg20 ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT A bound on the approximation of a Catmull-Clark subdivision surface by its limit mesh Zhangjin Huang a,b,∗, Jiansong Deng c , Guoping Wang a aSchool of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China bDepartment of Computer Science and Technology, University of Science and Technology of China, Hefei, Anhui 230027, China cDepartment of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China Abstract A Catmull-Clark subdivision surface (CCSS) is a smooth surface generated by re￾cursively refining its control meshes, which are often used as linear approximations to the limit surface in geometry processing. For a given control mesh of a CCSS, by pushing the control points to their limit positions, another linear approximation – a limit mesh of the CCSS is obtained. In general a limit mesh might approximate a CCSS better than the corresponding control mesh. We derive a bound on the distance between a CCSS patch and its limit face in terms of the maximum norm of the second order differences of the control points and a constant that depends only on the valence of the patch. A subdivision depth estimation formula for the limit mesh approximation is also proposed. For a given error tolerance, fewer subdivision steps are needed if the refined control mesh is replaced with the corresponding limit mesh. Key words: Catmull-Clark subdivision surfaces, Limit mesh, Distance bound, Subdivision depth ∗ Corresponding author. Tel.: +86 10 62765819; fax: +86 10 62755798. Email addresses: zhangjin.huang@gmail.com (Zhangjin Huang), dengjs@ustc.edu.cn (Jiansong Deng), gwang@graphics.pku.edu.cn (Guoping Wang). Preprint submitted to Elsevier 29 May 2008